In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: \t\t\tu(s)=ϕi(s)+∫abKi(s,r,u(r))dr,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$u(s)=\\phi_{i}(s)+ \\int_{a}^{b}K_{i}\\bigl(s, r,u(r)\\bigr) \\,dr, $$\\end{document} where sin(a,b)subseteqmathbb{R}; u, phi_{i}in C((a,b),mathbb{R}^{n}) and K_{i}:(a,b)times(a,b)times mathbb{R}^{n}rightarrowmathbb{R}^{n}, i=1,2,ldots,6 and \t\t\tu(s)=pi(s)+λ∫0tm(s,r)gi(r,u(r))dr+μ∫0∞n(s,r)hi(r,u(r))dr,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$u(s)=p_{i}(s)+\\lambda \\int_{0}^{t}m(s, r)g_{i}\\bigl(r,u(r) \\bigr)\\,dr+\\mu \\int_{0}^{\\infty}n(s, r)h_{i}\\bigl(r,u(r) \\bigr)\\,dr, $$\\end{document} where sin(0,infty), lambda,muinmathbb{R}, u, p_{i}, m(s, r), n(s, r), g_{i}(r,u(r)) and h_{i}(r,u(r)), i=1,2,ldots,6, are real-valued measurable functions both in s and r on (0,infty).